I'm told that you can sometimes see the bullet in flight.
^^^ This. Other folks in this thread have also mentioned seeing bullets in flight. Seeing them from the side would require a slowwww... bullet! But from a position directly behind the shooter, one can see faster bullets.
It's common to see the glint off the base of a .308 Win flying out to 500 yds. Sure, the velocity in the direction of travel is high, but the vertical component is slow as the bullet goes above the line of sight and then falls. Easy to see in a spotting scope if the light is right and you get the "glint." I also commonly see 22 LR slugs in my rifle scope or in a spotting scope behind the shooter in our 200 meter matches. Sure helps in spotting for a shooter.